A class of freeform gradient index (GRIN) optics rely on axial, radial, or three-dimensionally varying concentrations of one or more organic or inorganic materials which result in nonhomogeneous complex dielectric properties throughout the material. For instance, the refractive-index can be varied so light refracts not only at the air-optic interface, but also refract within the nonhomogeneous 3D gradient index optical material. Advances in material and manufacturing technologies have allowed for drop-on-demand manufacture of such GRIN optics with nanocomposite-inks. One example of which includes traditional inkjet printing.
Traditional inkjet printing applications include printing one or more colored inks on paper or other substrates to reproduce imagery by reflectance or light scattering from the deposited ink and substrate in order to reproduce imagery. In order to produce continuous tones or colors, a multitude of colored inks would be required. Instead, a limited amount of ink colors, in combination with the substrate color, are used to simulate greyscale and color tones using techniques such as halftoning and dithering.
The classical halftoning technique, usually synonymous with amplitude modulation halftoning, uses dots of varying size or spacing to represent intensities. In either case, the dots of various size and/or spacing are generally below the resolving power of the human eye in order to replicate an illusion of a continuous tone image with limited inks. For instance, a continuous transition from white to black can be replicated by gradually increasing black ink dot size, decreasing dot spacing, or both on a white substrate. From a sufficient distance away, the human vision system interpret the dots as a smooth transition.
Dithering, a technique also known as color quantization, is a more general term that refers to randomization or perturbation of colors values, positions, or intensity in order to simulate more tones than are truly available. Generally, dithering is the process of using two colors to simulate the shade of a third color by placing dots of two colors close together on a substrate, the substrate typically white. The dithering process can use several strategies of placing the dots over the region showing the third color. In a dithered image, colors that are not available in the palette are approximated by a depositing grouping of colored droplets. The droplets are typically spatially discrete or slightly overlapping, with areas of the substrate exposed. The human vision system perceives the droplet groupings as a diffusion of the colored droplets and substrate.
Dithering and halftoning rely on the psychophysics of the human eye and neural processing system into perceiving more colors than are there. The human eye perceives the droplets as a mixture of the colors within. The more dither patterns that a device or program supports, the more color tones or shades of gray it can represent.
Every printer has a native internal pixel resolution that printed images will be resampled to. Many commercial printers have a capability to print drops at up to 4800 dpi (dots per inch), although the visible optical resolution is between 600 and 720 ppi (pixels per inch). The tonal range that may be reproducible by a printer is ultimately determined by the cell size of a pixel.
Unlike for printed materials visible to the human eye, there has yet to be well established methods of printing optical inks to achieve a gradient optical index with using two or more specific optical index inks fewer in number than that required by the gradient. Traditional inkjet printing applications include color printing on paper or other substrates. In inkjet printing, imagery is simulated by techniques such as halftoning and dithering. The halftoning technique deposits droplets in dots, or pixels, of various size and/or spacing in order to replicate a continuous tone image, for instance, a continuous transition from white to black can be replicated by gradually increasing dot size, decreasing dot spacing, or both. From a sufficient distance away, the human vision system interpret the dots as a smooth transition. In printing optical materials, wherein sub-wavelength features are important to achieve high modulation transfer functions (MTF), the halftoning methods developed to satisfy the human eye may not be optimal.